High Dimensional Visualization By Mingyue Tan Mar10, 2004.

High Dimensional Visualization

By

Mingyue TanMar10, 2004

High Dimensional Data

High-D data:- ungraspable to a

human’s mind What does a 10-D space look like?

We need effective multi-D

visualization techniques

Paper Reviewed Dimensional Anchors: a Graphic Primitive for

Multidimensional Multivariate Information Visualizations, P. Hoffman, G. Grinstein, & D. Prinkney, Proc. Workshop on New Paradigms in Information Visualization and Manipulation, Nov. 1999, pp. 9-16.

Visualizing Multi-dimensional Clusters, Trends, and Outliers using Star Coordinates, Eser Kandogan, Proc. KDD 2001

StarClass: Interactive Visual Classification Using Star Coordinates , S. Teoh & K. Ma, Proc. SIAM 2003

Dataset Car - contains car specs (eg. mpg, cylinders, weight,

acceleration, displacement, type(origin), horsepower, year, etc)

- type: American, Japanese, & European

Dimensional Anchors (DA)Dimensional Anchor: Attempt to unify many different multi-var

visualizations Uses of 9 DA parameters

Base Visualizations Scatter Plot Parallel Coordinates Survey Plot Radviz spring visualization

Parallel Coordinates Point -> line (0,1,-1,2)=

0

x

0

y

0

z

0

w

Base Visualizations Scatter Plot Parallel Coordinates Survey Plot Radviz spring visualization

Parameters ofDA

Nine parameters are selected to describe the graphics properties of each DA:

p1: size of the scatter plot points p2: length of the perpendicular lines extending from individual

anchorpoints in a scatter plot p3: length of the lines connecting scatter plot points that are

associated with the same data point p4: width of the rectangle in a survey plot p5: length of the parallel coordinate lines p6: blocking factor for the parallel coordinate lines p7: size of the radviz plot point p8: length of the “spring” lines extending from individual

anchorpoints of a radviz plot p9: the zoom factor for the “spring” constant K

Basic Single DA

•Dimension – miles per gallon•Data values are mapped to the axis• Mapped data points - anchorpoints, represent the coord values(points along a DA)•Lines extended from anchorpoints•Color – type of car (American – red, Japanese – green, and European – purple)

Two-DA scatter plotDA scatter plot using two DAs Perpendicular lines extending

outward from the anchor points

If they meet, plot the point at the intersection

p1: size of the scatter plot points

p2: length of the perpendicular lines extending from individual anchor points in a scatter plot

p3: length of the lines connecting scatter plot points that are associated with the same data point P = (0.8, .2, 0, 0, 0, 0, 0, 0,

0)

Three DAs

P = (0.6, 0, 0, 0, 0, 0, 0, 0, 0)

P = (.6, 0, 1.0, 0, 0, 0, 0, 0, 0)P3: length of lines connecting all displayed points

associated with one real data point(record)

Seven DA Survey Plot 7 vertical DAs in a row Rectangle extending

from an anchor point - size is based on the

dimensional value - eg. Type- discrete

value red < green <

purple

CCCViz – Color Correlated Column Does a dimension

(gray scales) correlate with a particular classification dimension(color scale) ?

Correlation is seen in mpg, cylinders etc.

p4: width of the rectangle in a survey plot CCCViz DAs with P = (0, 0, 0,

1.0, 0, 0, 0, 0, 0)

DAs in PC configuration Line from one DA

anchorpoint is drawn to another

- length of these connecting lines is controlled by p5.

- p5 = 1.0, fully connected, every anchorpoint connects to all the other (N-1) anchorpoints

P6 controls how many DAs a p5 connecting line can cross

- p6 = 0, traditional PCP = (0, 0, 0, 0, 1.0, 1.0, 0, 0,

0)

DAs in Regular Polygon

Intro. to RadViz Spring Force a radial visualization One spring for each

dimension. One end attached to

perimeter point. The other end attached to a data point.

Each data point is displayed where the sum of the spring forces equals 0.

DAs RadViz

Original Radviz – 3 overlapping points DAs spread polygon P = (0, 0, 0, 0, 0, 0, .5,

1.0, .5)Limitation: data points with different values can overlap

DA layout Parameters – Done ! Layout - DAs can be

arranged with any arbitrary size, shape or position

- Permits a large variety of visualization designs

Combinations of Visualizations Can we combine

features of two (or more) visualizations?

Combination of Parallel Coordinates and Radviz

Visualization Space Nine parameters define the size of our

visualization space as R9

Include the geometry of the DAs, assuming 3 parameters are used to define the geometry

The size of our visualization space is R12

“Grand Tour” through visualization space is possible

New visualizations can be created during a tour

EvaluationStrong Points Idea Many examples of

visualizations with real data

Weak Points Not accessible Short explanation of

examples Lack of examples for

some statement No implementation

details

Where are we Dimensional Anchors

Star Coordinates - a new interactive multidimensional

technique - helpful in visualizing multi-dimensional

clusters, trends, and outliers

StarClass – Interactive Visual Classification Using Star Coordinates

Star Coordinates Each dimension shown

as an axis Data value in each

dimension is represented as a vector.

Data points are scaled to the length of the axis

- min mapping to origin - max mapping to the

end

Star Coordinates ContdCartesian Star Coordinates

P=(v1, v2) P=(v1,v2,v3,v4,v5,v6,v7,v8)

Mapping:• Items → dots• Σ attribute vectors → position

v1

v2

d1

p

Interaction Features Scaling - allows user to change the length of an axis

- increases or decrease the contribution of a data column Rotation - changes the direction of the unit vector of an axis - makes a particular data column more or less correlated

with the other columns Marking - selects individual points or all points within a rectangular

area and paints them in color - makes points easy to follow in the subsequent

transformations

Interaction Features Range Selection - select value ranges on one or more axes, mark

and paint them - allows users to understand the distribution of

particular data value ranges in current layout

Histogram - provides data distribution for each dimension

Footprints - leave marks of data points on the trail for recent transformations

Applications – Cluster Analysis Playing with the

“cars” dataset - scaling,

rotating, & turning off some coordinates

Four major clusters in the data discovered

Applications – Cluster Analysis

Scaling the “origin” coordinate moves only the top two clusters

- (JP & Euro) Down-scaling the origin - these two clusters

join one of the other clusters(American-made cars of similar specs)

Result: two clustersLow weight,

displacement, high acceleration cars

SC – useful in visualizing clusters Within few minutes users can identify

how the data is clustered Gain an understanding of the basic

characteristics of these clusters

Multi-factor Analysis Dataset – “Places” - ratings wrt climate,

transportation, housing, education, arts, recreation, crime, health-care, and economics

Important desirable factors pulled together in one direction and neg. undesirable factors in the opposite

Mutli-factor Analysis con’t Desirable factors: - recreation, art, &

education - climate (most) Undesirable factor: - crime

What can you conclude about NY and SF?

•NY – outlier•SF – comparable arts, ect, but better climate and lower crime

Multi-factor Analysis contd

Scale up transportation

- other cities beat SF in the combined measure

Evaluation of SC in Multi-factor Analysis Exact individual contributions of these factors are not

immediately clear

The visualization provides users with an overview of how a number of factors affect the overall decision making

EvaluationStrong Points idea many concrete

examples with full explanations

Weak points ugly figures

(undistinguishable)

Where we are Dimensional Anchors

Star Coordinates - a new interactive multi-D visualization

tech. StarClass – Interactive Visual Classification

Using Star Coordinates

Classification Each object in a dataset belongs to exactly

one class among a set of classes. Training set data : labeled (class known) Build model based on training set Classification: use the model to assign a

class to each object in the testing set.

Classification Method Decision trees 

Class2 Class 3

Visual-base DT Construction Visual Classification - projecting - painting - region can be re-projected

- recursively define a decision tree.

- each project correspond to a node in decision tree

- Majority class at leaf node determines class assignment

(the class with the most number of objects mapping to a terminal region is the “expected class”)

Evaluation of the system

Makes use of human judgment and guides the classification process

Good accuracy Increase in user’s

understanding of the data

expertise required?

Good Bad

Evaluation of the PaperGood Ideas Accessible Concrete examples

Bad No implementation

discussed

Summary Dimensional Anchor - unify visualization techniques Star Coordinate - new interactive visualization techniques - Visualizing clusters and outliers StarClass - interactive classification using star coordinate

Reference Dimensional Anchors: a Graphic Primitive for

Multidimensional Multivariate Information Visualizations, P. Hoffman, G. Grinstein, & D. Prinkney, Proc. Workshop on New Paradigms in Information Visualization and Manipulation, Nov. 1999, pp. 9-16.

Visualizing Multi-dimensional Clusters, Trends, and Outliers using Star Coordinates, Eser Kandogan, Proc. KDD 2001

StarClass: Interactive Visual Classification Using Star Coordinates , S. Teoh & K. Ma, Proc. SIAM 2003

http://graphics.cs.ucdavis.edu/~steoh/research/classification/SDM03.ppt